In an acid-base titration,the rapid change in $pH$ near the equivalence point depends on the indicator used. The $pH$ of the solution is related to the ratio of the concentrations of the conjugate acid $(HIn)$ and base $(In^-)$ forms of the indicator by which equation?

The titration curve of a weak acid vs. a strong base with phenolphthalein as an indicator is shown below. The $K_{In} = 4 \times 10^{-10}$. Given: $\log 2 = 0.3$. The number of the following statements which is/are correct about phenolphthalein is $.....$.
$A$. It can be used as an indicator for the titration of a weak acid with a weak base.
$B$. It begins to change colour at $pH = 8.4$.
$C$. It is a weak organic base.
$D$. It is colourless in an acidic medium.

For an acid indicator with $K_{in} = 1.0 \times 10^{-5}$, the color change occurs when the concentration of the indicator is $1 \times 10^{-3} \ M$. Find the $pH$ at which the color change occurs.

The $pH$ range of methyl red indicator is .......?

The pink colour of phenolphthalein in an alkaline medium is due to -

At what $pH$ will an indicator with $K_b = 1 \times 10^{-11}$ show a color change in a $1 \times 10^{-4} \ M$ solution?